# Magnet (unidirectional): demagnetization curve (Hc, Br) + knee

## Presentation

This model ( Nonlinear magnet described by H c and the B r module, plus knee adjustment ) defines a nonlinear B(H) dependence with taking into account of demagnetization and knee adjustment .

Main characteristics:

- the mathematical model and the direction of magnetization are dissociated
- a single material for description of several regions

## Mathematical model

In the direction of magnetization the model is a combination of a straight line and an arc tangent curve . A coefficient adjusts the shape of the curve knee for a better approximation of the experimental curve

The corresponding mathematical formula is written:

with

where:

- μ
_{0}is the permeability of vacuum, μ_{0}= 4 π 10^{-7}H/m - μ
_{r}is the relative permeability of material (for H = H_{c}) - H
_{c}is the coercive field strength A/m - a is the knee adjustment coefficient (0 < a and a < > 1)

The smaller the coefficient, the sharper the knee is.

- J
_{s'}is computed by dichotomy from B_{r}, H_{c}and μ_{r}, with the equation

The shape of the B(H) dependence in the direction of magnetization is given in the opposite figure.

In transversal directions one can write:

B_{⊥}(H) = μ_{0}μ_{r⊥}H_{⊥}

where
μ_{r⊥} is the transverse relative permeability

## Direction of magnetization

The various possibilities provided to the user are the same ones as those presented in § Magnet (unidirectional): linear approximation.